Spatial Bayesian Factor Analysis

Implements a spatial Bayesian non-parametric factor analysis model with inference in a Bayesian setting using Markov chain Monte Carlo (MCMC). Spatial correlation is introduced in the columns of the factor loadings matrix using a Bayesian non-parametric prior, the probit stick-breaking process. Areal spatial data is modeled using a conditional autoregressive (CAR) prior and point-referenced spatial data is treated using a Gaussian process. The response variable can be modeled as Gaussian, probit, Tobit, or Binomial (using Polya-Gamma augmentation). Temporal correlation is introduced for the latent factors through a hierarchical structure and can be specified as exponential or first-order autoregressive. Full details of the package can be found in the accompanying vignette. Furthermore, the details of the package can be found in "Bayesian Non-Parametric Factor Analysis for Longitudinal Spatial Surfaces", by Berchuck et al (2019), . The paper is in press at the journal Bayesian Analysis.

Post-Processing MCMC Outputs of Bayesian Factor Analytic Models

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to generate samples from the posterior distribution. The package applies a series of rotation, sign and permutation transformations (Papastamoulis and Ntzoufras (2022) ) into raw MCMC samples of factor loadings, which are provided by the user. The post-processed output is identifiable and can be used for MCMC inference on any parametric function of factor loadings. Comparison of multiple MCMC chains is also possible.

Bayesian Tensor Factorization

Bayesian Tensor Factorization for decomposition of tensor data sets using the trilinear CANDECOMP/PARAFAC (CP) factorization, with automatic component selection. The complete data analysis pipeline is provided, including functions and recommendations for data normalization and model definition, as well as missing value prediction and model visualization. The method performs factorization for three-way tensor datasets and the inference is implemented with Gibbs sampling.

Bayesian Inference for Factor Modeling

Collection of procedures to perform Bayesian analysis on a variety of factor models. Currently, it includes: "Bayesian Exploratory Factor Analysis" (befa) from G. Conti, S. Frühwirth-Schnatter, J.J. Heckman, R. Piatek (2014) , an approach to dedicated factor analysis with stochastic search on the structure of the factor loading matrix. The number of latent factors, as well as the allocation of the manifest variables to the factors, are not fixed a priori but determined during MCMC sampling.

Bayesian Infinite Factor Models

Sampler and post-processing functions for semi-parametric Bayesian infinite factor models, motivated by the Multiplicative Gamma Shrinkage Prior of Bhattacharya and Dunson (2011) < https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3419391/>. Contains component C++ functions for building samplers for linear and 2-way interaction factor models using the multiplicative gamma and Dirichlet-Laplace shrinkage priors. The package also contains post processing functions to return matrices that display rotational ambiguity to identifiability through successive application of orthogonalization procedures and resolution of column label and sign switching. This package was developed with the support of the National Institute of Environmental Health Sciences grant 1R01ES028804-01.

A Bayesian Semiparametric Factor Analysis Model for Subtype Identification (Clustering)

Gene expression profiles are commonly utilized to infer disease subtypes and many clustering methods can be adopted for this task. However, existing clustering methods may not perform well when genes are highly correlated and many uninformative genes are included for clustering. To deal with these challenges, we develop a novel clustering method in the Bayesian setting. This method, called BCSub, adopts an innovative semiparametric Bayesian factor analysis model to reduce the dimension of the data to a few factor scores for clustering. Specifically, the factor scores are assumed to follow the Dirichlet process mixture model in order to induce clustering.

Understand and Describe Bayesian Models and Posterior Distributions

Provides utilities to describe posterior distributions and Bayesian models. It includes point-estimates such as Maximum A Posteriori (MAP), measures of dispersion (Highest Density Interval - HDI; Kruschke, 2015 ) and indices used for null-hypothesis testing (such as ROPE percentage, pd and Bayes factors). References: Makowski et al. (2021) .

Bayesian Dynamic Factor Analysis (DFA) with 'Stan'

Implements Bayesian dynamic factor analysis with 'Stan'. Dynamic factor analysis is a dimension reduction tool for multivariate time series. 'bayesdfa' extends conventional dynamic factor models in several ways. First, extreme events may be estimated in the latent trend by modeling process error with a student-t distribution. Second, alternative constraints (including proportions are allowed). Third, the estimated dynamic factors can be analyzed with hidden Markov models to evaluate support for latent regimes.

Bayesian Model Selection with Suspected Latent Grouping Factors

Implements the Bayesian model selection method with suspected latent grouping factor methodology of Metzger and Franck (2020), . SLGF detects latent heteroscedasticity or group-based regression effects based on the levels of a user-specified categorical predictor.

Bayesian Estimation of (Sparse) Latent Factor Stochastic Volatility Models

Markov chain Monte Carlo (MCMC) sampler for fully Bayesian estimation of latent factor stochastic volatility models with interweaving . Sparsity can be achieved through the usage of Normal-Gamma priors on the factor loading matrix .